Model reduction for compressible flows using POD and Galerkin projection

Rowley, Clarence W.; Colonius, Tim; Murray, Richard M.

doi:10.1016/j.physd.2003.03.001

Cited by 699 publications

(462 citation statements)

References 11 publications

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“…Here, the OID induces weights in the bilinear form via the standard inner product of the linearly related observables. Alternatively, these weights can be chosen directly (see Rowley, Colonius & Murray 2004;Rowley 2005) or by design of optimal control functionals (see Tröltzsch 2005). Via the null space of the bilinear form, design flexibility of the 'observable' OID subspace is provided, enabling OID variants like LR-and LE-OID tailored for purposes of flow control.…”

Section: Discussionmentioning

confidence: 99%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, leastbiased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a 'least-residual' variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the 'least-energetic' variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; † Email address for correspondence: michael.schlegel@tu-berlin.de

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Section: Discussionmentioning

confidence: 99%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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“…The POD/Galerkin method has been used extensively for reduced-order modeling of fluid problems [13,23,31,34,35]. In this method, an empirical basis of orthonormal eigenfunctions is obtained from experimental or simulation data, and the Navier-Stokes equations are projected onto this basis.…”

Section: Introductionmentioning

confidence: 99%

Modeling of transitional channel flow using balanced proper orthogonal decomposition

2008

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We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to the traditional single-wavenumber approach, and are therefore better able to capture the effects of localized disturbances or localized actuators. In order to assess the performance of the models, we consider the impulse response and frequency response, and variation of the Reynolds number as a model parameter. We show that the BPOD procedure yields models that capture the transient growth well at a low order, whereas standard POD does not capture the growth unless a considerably larger number of modes is included, and even then can be inaccurate. In the case of a localized actuator, we show that POD modes which are not energetically significant can be very important for capturing the energy growth. In addition, a comparison of the subspaces resulting from the two methods suggests that the use of a non-orthogonal projection with adjoint modes is most likely the main reason for the superior performance of BPOD. We also demonstrate that for single-wavenumber perturbations, low-order BPOD models reproduce the dominant eigenvalues of the full system better than POD models of the same order.These features indicate that the simple, yet accurate BPOD models are a good candidate for developing model-based controllers for channel flow.

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“…Collecting, at a given sequence of time instants t k , timesnapshots (which resemble the ones used to compute a proper orthogonal decomposition (POD), see e.g. [28], [29], [30], [31]) of the input and output of the system, an algorithm is devised to define a family of reduced order models (in the framework introduced in [18]) at each instant of the iteration t k . The reduced order model asymptotically matches the moments of the unknown system to be reduced.…”

Section: Introductionmentioning

confidence: 99%

Model reduction for linear systems and linear time-delay systems from input/output data

Scarciotti

Astolfi

2015

2015 European Control Conference (ECC)

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Abstract-An algorithm for the estimation of the moments of linear single-input, single-output (SISO) systems and linear time-delay SISO systems from input/output data is proposed. It is proved that the estimate converges to the moments of the system. The estimate is exploited to construct a family of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. Conditions to enforce additional properties, e.g. matching with prescribed eigenvalues or matching with prescribed zeros, upon the reduced order model are provided and discussed. The computational complexity of the algorithm is analyzed and the use of the algorithm is illustrated by a benchmark example.

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Model reduction for compressible flows using POD and Galerkin projection

Cited by 699 publications

References 11 publications

On least-order flow representations for aerodynamics and aeroacoustics

On least-order flow representations for aerodynamics and aeroacoustics

Modeling of transitional channel flow using balanced proper orthogonal decomposition

Model reduction for linear systems and linear time-delay systems from input/output data

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